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Formulate the recursive formula for the following geometric sequence. {-16, 4, -1, ...} ?

Answer 1

Anna Allen

#a_n=-16(-1/4)^n, n={0,1,2,3,cdots}#

We have the sequence #{-16,4,-1,cdots}#

We can already discern a pattern by examining the sequence's first three terms.

Each term is divided by four and has its sign reversed starting at -16.

Thus, the series can be expressed as follows:

#{-16, -16(-1/4), -16(-1/4)^2,cdots}#

So the formula for the #n#th term of the sequence is

#a_n=-16(-1/4)^n, n={0,1,2,3,cdots}#

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Answer 2

Sadie Alexander

The recursive formula for the given geometric sequence is:

( a_{n+1} = \frac{a_n}{-4} )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.